The present invention relates to a device and method for sending symbols and to a device and method for receiving symbols.
It deals more precisely with the technique of direct sequence spread spectrum, or xe2x80x9cDSSSxe2x80x9d. This method is a data transmission method in which the band width used is wider than that which is required by the flow of information. In place of the transmission of an information symbol every T seconds (situation xe2x80x9c1xe2x80x9d), here a symbol is transmitted every T/n seconds with the additional constraint that, the set of n symbols transmitted between times i. T and (i+1). T (i being integer), the first transmitted symbols greatly reduce the possible values of the last symbols transmitted (situation xe2x80x9c2xe2x80x9d).
The sequence of n xe2x80x9cshortxe2x80x9d symbols which replaces a single xe2x80x9clong xe2x80x9d symbol is referred to as the spread sequence.
After modulation (amplitude, phase, quadrature amplitude etc) of a carrier, the resulting power spectrum is different between situations 1 and 2:
typically, in situation 1, the power spectrum is narrow but has a high value in this narrow range. Conversely, in situation 2, the power spectrum is wider (by a factor of approximately n) and it has a low value over this wide range. An advantage of situation 2 compared with situation 1 is that it makes the transmission more resistant to frequency-dependent noise and fading due to the multiple propagation paths of the translated signals. In fact situation 2 better distributes the transmission power as a function of spread spectrum is made compulsory by many current regulations.
When a spread sequence is received after transmission over a channel, the receiver will have to estimate the corresponding information. It is known that this task is easier and can be carried out more effectively when the transmitted sequences are chosen from a set of sequences obtained from a set of sequences which are orthogonal in pairs, by multiplying each of these sequences on the one hand by xe2x80x9c+1xe2x80x9d and on the other hand by xe2x80x9cxe2x88x921xe2x80x9d (this second product supplying a sequence which is said to be the xe2x80x9coppositexe2x80x9d of the multiplied sequence).
Considering, for example, a channel accepting at its input signals which are amplitude modulated proportionally to any one of the numbers of the alphabet A={xe2x88x927, xe2x88x925, xe2x88x923, xe2x88x921, 1, 3, 5, 7}. This is then referred to as an 8-AM modulation. It will in this case be wished to construct a set of sequences x=(x1, . . . , xn) of length n on the alphabet A and to represent the information to be transmitted by a succession of such sequences x. As indicated above, each sequence x of n short symbols xi can be used to replace a single long symbol. To achieve the same flow of information in replacing each of the eight xe2x80x9clongxe2x80x9d symbols of A by a different sequence of length n on A, whilst making use of certain properties of orthogonality between different sequences, it suffices for example to be capable of constructing four different sequences of length n on the alphabet A. If v1, v2, v3 and v4 are these four sequences and if the four sequences v5=xe2x88x92v1, v6=xe2x88x92v2, v7=xe2x88x92v3 and v8=xe2x88x92v4 are added to all these four sequences, there are in fact eight sequences of length n on A. If vi and vj are two different sequences amongst these eight sequences and if they are not orthogonal to each other, then they satisfy vi=xe2x88x92vj. These properties are important since they permit a simple estimation of the transmitted sequence, by correlating the received sequence with each of the four sequences v1, v2, v3 and v4.
This number of four sequences which are orthogonal in pairs is therefore sufficient in the example under consideration. However, when four such sequences which are orthogonal in pairs can be constructed, of length n greater than 4, it is sometimes possible to construct more of them and even to construct the maximum number of them, namely n. This is not without interest since the additional available sequences make it possible to increase the transmitted information rate. If in fact k such sequences are available, where k is an integer verifying 4 less than kxe2x89xa6n, it is in fact well known that this makes it possible to multiply the channel transmission rate, measured in bits per second, by a factor ((log2(2k))/3, compared with the case where only the 8 signals of the alphabet A are used without spread during each interval of T seconds.
The construction of n sequences which are orthogonal in pairs, of length n on the alphabet A, amounts to constructing a matrix H of type nxc3x97n on A, such that all the elements of the principal diagonal of the matrix equal to the matrix product of H and its transposition HT are non-nil and all the elements outside this principal diagonal are nil.
The case where all the non-nil values of H.HT are equal (that is to say H.HT=M.In where In is the identity matrix nxc3x97n) is particularly interesting since it corresponds to the case where the energy of the signal which is amplitude modulated by the sequence associated with each line of H, is identical. The matrix H is then said to be xe2x80x9cbalancedxe2x80x9d.
Such matrices H on the alphabet A such that H.HT=M.In have actually been constructed by the inventor but only for values of n which are multiples of 4. However, it is clear that, in some applications, more general values of n are necessary. In particular the case where n=10 is very interesting because it corresponds to the minimum spread factor required by certain regulations. However, in the case n=10, it can be demonstrated that there is no matrix with 10 rows and 10 columns on the alphabet A which satisfies H.HT=M.I10, with M greater than 0.
The present invention relates, according to a first aspect, to a method of transmitting on a transmission channel, characterised in that it includes an operation of sending, on the said channel, sequences of a fixed length which is not a multiple of 4, symbols taken from an alphabet of non-nil integers, the said sequences being taken from a collection of sequences in which at least three are orthogonal in pairs and such that any pair of sequences which are not orthogonal to each other consist of opposite sequences.
It should be stated here that two sequences are said to be xe2x80x9coppositexe2x80x9d when their homologous terms (that is to say with the same ranking in the two sequences) are opposite.
By virtue of these provisions, the sequences of transmitted symbols benefit, on reception, from the effects of their orthogonality or opposition, whereas, prior to the present invention, no orthogonal matrix was known with the characteristics of having dimensions which are not multiples of 4 on the one hand and having been constructed on an alphabet of non-nil integers on the other hand.
Thus the idea at the basis of the invention is, in the example mentioned above, using the alphabet A*={xe2x88x924, xe2x88x923, xe2x88x922, xe2x88x921, +1, +2, +3, +4} in place of the alphabet A.
As the elements of the alphabets (A,A*, . . . ) define the physical quantities transmitted on the channel only to within a factor of proportionality, it will be noted that two alphabets are equivalent if one of them can be derived from the other by multiplying all its elements by a fixed quantity. Thus the alphabet A* is equivalent to the alphabet B*={xe2x88x928, xe2x88x926, xe2x88x924, xe2x88x922, +2, +4, +6, +8}, which is obtained by multiplying each of the symbols of the alphabet A* by two. The alphabet B* is also obtained by adding the value 1 to the absolute value of each of the symbols of the alphabet A.
The invention uses this alphabet A* for the transmission of information.
According to particular characteristics, the said collection includes a number of sequences which are orthogonal in pairs, equal to the length of the said sequences.
It will in fact be demonstrated below that the alphabet A* makes it possible to produce matrices with 10 rows and 10 columns satisfying:
H.HT=M I10xe2x80x83xe2x80x83(1)
By virtue of these provisions, the number of sequences of the collection which are orthogonal in pairs is at a maximum, which makes it possible to take greatest advantage of the constraint of orthogonality or opposition of the sequences in order to transmit a maximum quantity of information on the said channel.
According to particular characteristics, the said alphabet includes all the non-nil integers whose absolute value is less than a predetermined value.
By virtue of these provisions, the alphabet used is particularly simple and the components used for sending modulated sequences of symbols of this alphabet are also particularly simple to use.
According to particular characteristics, a matrix formed by the said orthogonal sequences can be broken down into circulant square sub-matrices.
By virtue of these provisions, the said matrix is determined by determining, in an intermediate step, of such sub-matrices, which is more simple since on the one hand the dimensions of the sub-matrices are necessarily less than those of the matrix, and on the other hand the circulant sub-matrices are specified by the elements of their first row, these two considerations considerably reducing the number of matrices to be considered.
According to a second aspect, the present invention relates to a method of receiving on a transmission channel, characterised in that it includes:
an operation of receiving, on the said channel, sequences with a fixed length which is not a multiple of 4, and
an operation of estimating the said sequences in sequences of symbols taken from an alphabet of non-nil integers, the said sequences being taken from a collection of sequences, at least three of which are orthogonal in pairs and such that any pair of sequences which are not orthogonal to each other consists of opposite sequences.
According to a third aspect, the present. invention relates to a method of transmitting on a transmission channel, characterised in that it includes an operation of sending, on the said channel, numbers which are multiples of all the non-nil integers whose absolute value is less than a predetermined value.
According to a fourth aspect, the present invention relates to a device for transmitting on a transmission channel, characterised in that it has:
a processing means adapted to associate, with information to be transmitted, at least one sequence with a fixed length which is not a multiple of 4, of symbols taken from an alphabet of non-nil integers, the said sequences being taken from a collection of sequences, at least three of which are orthogonal in pairs and such that any pair of sequences which are not orthogonal to each other consist of opposite sequences, and
a sending means adapted to send, on the said channel, each of the said sequences.
According to a fifth aspect, the present invention relates to a device for receiving on a transmission channel, characterised in that it includes:
a means of receiving, on the said channel, sequences with a fixed length which is not a multiple of 4, and
a means of estimating the said sequences in sequences of symbols taken from an alphabet of non-nil integers, the said sequences being taken from a collection of sequences, at least three of which are orthogonal in pairs and such that any pair of sequences which are not orthogonal to each other consists of opposite sequences.
According to a sixth aspect, the present invention relates to a device for transmitting on a transmission channel, characterised in that it has a means of sending on the said channel adapted to send solely numbers which are multiples of all the non-nil integers whose absolute value is less than a predetermined value.
The invention also relates to a camera, a facsimile machine, a photographic apparatus, a computer, characterised in that they have a device as briefly disclosed above.
The invention also relates to:
a means of storing information which can be read by a computer or microprocessor storing instructions of a computer program, characterised in that it permits the implementation of the method of the invention as briefly disclosed above,
a means of storing information which can be read by a computer or microprocessor storing data resulting from the implementation of the method as briefly disclosed above,
a means of storing information which can be removed, partially or totally, and which can be read by a computer or microprocessor storing instructions of a computer program characterised in that it permits the implementation of the method of the invention as briefly disclosed above, and
a means of storing information which can be removed, partially or totally, and which can be read by a computer or microprocessor storing data resulting from the implementation of the method as briefly disclosed above.
The preferential or particular characteristics and the advantages of the transmission devices and methods, of the receiving device and method, of this camera, of this facsimile machine, of this photographic apparatus, of this computer and of these information storage means being identical to those of the transmission method, these advantages are not repeated here.